On 23.09.2021 09:39, Juho Laatu wrote:

If you use your first suggestion, then every Condorcet method is equal
in the eyes of point 2, so "using the same submethod" doesn't really
make sense. I suppose you're referring to the case where step one is
e.g. "Arrange a minmax election" and then round two only happens if
enough people complain about it.

voters' willingness to petition for a second round is what enables it to
distinguish an okay winner from a truly horrible one. However, if I were
to argue against it, I would probably say that voting isn't narrowly
utilitarian to begin with (the well-known paradox of voting), and that
the mechanism is complex enough that it might lead to too much of a
status quo bias.

Or to put it differently, the idea is that there's enough of a
barrier/threshold to petitions, then a second round would only happen
when the first-round winner is a bad one. But it's not obvious how this
threshold should be adjusted. In one extreme case, you always hold a
runoff whenever the Smith set is larger than one. In another, it takes a
supermajority to hold the runoff. I would be more in favor of the former
than the latter, particularly if there's some time between the two
rounds so that the Smith set candidates have to defend themselves,
participate in debates, etc.

Another option I suggested to Forest goes like this:

1. Arrange a Condorcet election with a strategy-resistant method and a
   method wth good performance under honesty, e.g. Smith,IRV and Ranked
   Pairs (probably something even better can be constructed).
2. If the winners are the same (which happens whenever there's a CW, but
   also in some other cases), then that winner wins outright.
3. Otherwise arrange a two candidate runoff between the two winners.

Simple, it's not, but the methods could cover each other's weaknesses.
Taking this reasoning further, it should be possible to design "minmax
robust methods" that return two candidates so that the VSE after a
honest two-candidate runoff is the best possible, no matter the level of
strategy.

Well, in theory. Actually designing such a method with desirable
properties (monotonicity, etc) would be much harder :-)

-km

How about a runoff between the candidate with minimal max pairwise
opposition and the candidate with maximal minimum pairwise (inclusive)
support.

With complete rankings they're equivalent. But equal rankings and
truncations arising from strategy or indifference can make the runoff more
interesting.

El jue., 23 de sep. de 2021 8:11 a. m., Kristofer Munsterhjelm <
km_elmet@t-online.de> escribió:

Yes. If the second round will be always held when there is no Condorcet winner, then the first round only checks if there is a Condorcet winner.

Yes. The finer details of the first round are relevant only if the election may make the final decision already after the first round also when there is no Condorcet winner.

The method might allow petitions only when there is no Condorcet winner, and one presents a scenario and claim (mandatory!) that the outcome of the election may have changed because of strategic voting (or there is an exact tie). Petitions could be accepted only from the candidates. The idea is thus to have second rounds only when they appear to be necessary, i.e. not often, and not because people just want to have a second try. The criteria for having the second round should reflect this target.

With respect to utilities, it is true that Condorcet focuses on majorities and not utilities, and therefore there might be cases where voters have some interest in changing the winner to some "higher utility winner". I have no good idea on how to accommodate such original sincere preferences, but I sort of hope that if one of the candidates or his supporters try to fool the system at the first round, people will get angry, and want to punish that candidate at the second round, and will rank him lower in a large number of ballots (thereby demonstrating changes in candidate utilities between the two rounds).

Yes. My target is that people take the first round seriously, and feel safe to vote sincerely, since the possibility of the second round protects them. As a result almost all elections would not need the second round. The second round would be arranged only when the first round "is a bad one" (typically because of foul play). Typically a second round would be needed only when there is a (quite rare) top loop, and some serious strategic voting (burying), or serious fear of it.

Yes, it is important to adjust the second round threshold and criteria carefully. My target was that the second round would be arranged only when there is a clear risk that the end result changed because of strategic voting (or when there is an exact tie that we prefer to resolve this way). The best outcome would thus be a method that would on average have about 1.001 rounds, and 99% of the votes would be sincere. The threat of second round would be there just to keep the first round "civilised".

And also other candidates than the Smith set candidates. :-)

You could see the second round also only as a technical round where you consider the candidates to be already known, and you reserve time only for all the strategic discussions and discussions on what went wrong at the first round. Also here I'm hoping that the strategic candidates will be ranked lower at the second round (but realising that also some false claims of strategic voting might appear :-) ).

In both approaches it makes sense to use a method with good performance under honesty at the first round.

If there was a strategic three candidate cycle at the first round, maybe people would reject the candidate whose supporters tried to bury others, and it would be just a race between the other two top loop candidates, even if also the second round would use a ranked Condorcet method. Using a runoff between two candidates would make the second round free of strategic voting, but might introduce some strategic voting in the first round. A carefully chosen pair of methods at the first round might eliminate strategies nicely, but I'm not able to estimate right now, how good the combination that you presented would be from this point of view.

The philosophy of the two approaches is different. In your proposal the idea seems to be to use two methods to cancel most strategies out, and in my proposal to allow people to vote honestly at the first round. There would be a chance to vote strategically at the second round if the first round fails to be sincere enough. One could of course go on and use three rounds, starting from one with ideal performance with sincere votes, and then proceeding to some more strategy proof method (or combination of methods), and finally to a two candidate runoff. But of course also simplicity should have some weight, and this approach might be already too complex for most needs.

Yes. Have you checked if there are strategic possibilities, trying to push the election to the second round, trying to vote so that some appropriate two candidates would go to the second round? The most difficult case might be one with a sincere three candidate top loop. (Too difficult for me to get a grip of that right now. :-) )

From majority perspective, assuming a natural top loop of three candidates, picking two of them (or some others) for the second round must be hard. (VSE = Voter Satisfaction Efficiency)

Yes. Strategies are complex, and having two methods trying to fight together against various combinations of strategies, with different combinations of defences, makes it even more complex. You could say that I took the easy way out when proposing an approach where we just hope that people are sensible enough and do not use strategies, under the protection of the second round, under the threat of having to vote also at the second round, having their strategic plans revealed to other voters already at the first round, and paying a price if voters don't like their strategic games, and fearing that voters will bullet vote some better and more sincere candidate, or at least not vote for the strategists, or have some working counter strategies at the second round. :-)

In some societies people might be more inclined to use strategies and fear strategies of others more than in some other societies. The approach that I proposed hopefully makes it one step easier to vote honestly in both cases. In the best case it would be just a standard Condorcet election with no need to ever resort to the second round.

BR, Juho

I commented also to Kristofer on this kind of methods that combine to methods to find two potential winners for the second round. I think they have potential to eliminate many risks, but the strategic scenarios get quite complex. Scenarios where there is a sincere top loop of three candidates might be the most vulnerable scenario. Any of the candidate teams would have interest in picking certain two candidates for the second round. Maybe all teams would use similar strategies. This gets too difficult for me to comment right now.

In my proposal I hoped that people would give up strategic voting at the first round. The same could apply also in your proposed method, if people believe that the chosen two methods are likely to pick the best winner for the second round (if there will be a second round). Since your proposal makes some final decisions on who will be allowed to take part in the second round, that might give some additional incentive to use strategies already at the first round. I kept all the candidates in the second round to keep the feeling that "nothing is lost even if I vote honestly at the first round".

One reason to use the same method at the second round was that this way the other voters will know the planned strategy of the strategic voters at the second round. This makes it easier to apply appropriate counterstrategies, and to punish those voters/candidates that tried to fool the system. The idea is thus that if you try to vote strategically, you will not get the intended dishonest result, but there will be a second round where all your competitors will know your strategy, and may punish you.

I'm not able to estimate how well your proposed criteria would perform under various strategies. Maybe one can prove/demonstrate that your selection of criteria would provide good candidates for the second round, and eliminate some key strategies (also in cases where the leading three or more candidates are very similar). It seems there might be room for some "almost bullet proof" choices, but it may be difficult to prove it, since the "proof" gets quite complex here. :-)

BR, Juho

On 9/24/21 12:11 AM, Forest Simmons wrote:

That's a good point, because the information concealed by equal-rank
and/or truncation is information we don't have to begin with.

Suppose that we have two methods that feed into a runoff (as with my
suggestion). This system takes a strategic ranked ballot for the first
round and a honest Plurality-style ballot for the second. But by the
revelation principle, we can replace this by a DSV method that takes a
honest ballot as input and strategize on behalf of the voter in the
first round, and then votes according to that ballot on the second.

(This might be a good way to construct strategy-resistant methods.
Though ensuring properties like monotonicity hold through the DSV
algorithm is the really difficult part.)

But for a method like the one you're describing, that doesn't work
because the information that the DSV method would use is hidden behind
equal-rank. It would only work if the voter always submits a complete
(no equal rank or truncation) ballot to the DSV method itself.

As such, a runoff might be a good way to clear up ambiguities that come
from equal rank or truncation. If, in essence, the method says "these
incomplete ballots can either point to A being a good winner or B being
a good winner, which one is it?", then the runoff would let the voters
answer that question.

(Perhaps a manual runoff could also blunt the worst problems of Approval
by the same logic, i.e. asking "I don't know if X or Y are the best
candidates or if there's a Burr dilemma going on; could you clarify
which it is?". But I'm not sure how you'd do that in a cloneproof way.)

-km

Here's a slightly different approach ...

If there is no Condorcet winner in the first round, publish the inclusive
pairwise matrix M where the entry in row i and column j is the number of
ballots on which candidate i is ranked ahead of or equal to candidate j.
Note that M(i, i) is just the implicit approval of candidate i.

The random favorite probabilities are also published along with who the
winner would have been under winning votes (wv), margins, or losing votes
(lv) as measures of defeat strength (or lack thereof).

After deliberation the candidates vote (with weights proportional to the
probabilities mentioned above) to determine whether wv, margins, or lv will
be used to resolve a top cycle (should there be one) in the final round.

Note that wv and lv are decisive in their respective choices of B and C,
for the following ballot profile ....

49 C
26 A>B
25 B

whereas margins is ... well ...marginal.

In the case where sincere preferences were 49 C>B instead of 49C, a
majority of 51 would prefer wv since it elects the sincere CW.

In the case where sincere preferences are 25 B>A, a majority of 75 would
prefer that B not win ... and since Plurality prohibits A from winning this
means that those 75 prefer that C win. That majority has power to choose
losing votes as the measure of defeat strength (or lack thereof).

So in both cases a clear majority has the power to defend the sincere CW
... in the first case electing B despite the attack of the minority C
faction, and in the second case to motivate the potential defectors to stay
loyal to A, the sincere CW in that case.

I suspect that in general an appropriate choice among wv, margins, and lv
can greatly facilitate defending a sincere CW against a strategic attack
that would subvert the sincere result if not checked.

Once the voters learn that their insincere ballot manipulations are likely
to be futile if not counter productive, the first round will usually (if
not 99.9% of the time) suffice .... no second poll necessary.

Now let's look at margins in the ballot profile

48 C
28 A>B
24 B

The top cycle is ...

A>B (28 - 24)
B>C (52 - 48)
C>A (48 - 28)

B and C are still the clear respective winners under wv and lv, while the
margins winner is unclear since A defeats B by the same four point margin
as B's defeat of C.

Note that losing votes gives priority to pairwise defeats having the least
opposition to the decision ... the fewest "hard feelings" so to speak...
while winning votes gives priority to pairwise victories having the most
enthusiastic support.

Arguments about which is better based on these considerations are beside
the point ... in a given election the one that best defends the sincere
Condorcet Winner is the one we need!

FWS

El vie., 24 de sep. de 2021 1:39 p. m., Juho Laatu juho.laatu@gmail.com
escribió:

El 24 sep. 2021 1:39 p. m., "Juho Laatu" juho.laatu@gmail.com escribió:

wrote:

first round winner

and elect the second round winner

Yes. If the second round will be always held when there is no Condorcet
winner, then the first round only checks if there is a Condorcet winner.

Yes. The finer details of the first round are relevant only if the election
may make the final decision already after the first round also when there
is no Condorcet winner.

The method might allow petitions only when there is no Condorcet winner,
and one presents a scenario and claim (mandatory!) that the outcome of the
election may have changed because of strategic voting (or there is an exact
tie). Petitions could be accepted only from the candidates. The idea is
thus to have second rounds only when they appear to be necessary, i.e. not
often, and not because people just want to have a second try. The criteria
for having the second round should reflect this target.

With respect to utilities, it is true that Condorcet focuses on majorities
and not utilities, and therefore there might be cases where voters have
some interest in changing the winner to some "higher utility winner". I
have no good idea on how to accommodate such original sincere preferences,
but I sort of hope that if one of the candidates or his supporters try to
fool the system at the first round, people will get angry, and want to
punish that candidate at the second round, and will rank him lower in a
large number of ballots (thereby demonstrating changes in candidate
utilities between the two rounds).

Yes. My target is that people take the first round seriously, and feel safe
to vote sincerely, since the possibility of the second round protects them.
As a result almost all elections would not need the second round. The
second round would be arranged only when the first round "is a bad one"
(typically because of foul play). Typically a second round would be needed
only when there is a (quite rare) top loop, and some serious strategic
voting (burying), or serious fear of it.

Yes, it is important to adjust the second round threshold and criteria
carefully. My target was that the second round would be arranged only when
there is a clear risk that the end result changed because of strategic
voting (or when there is an exact tie that we prefer to resolve this way).
The best outcome would thus be a method that would on average have about
1.001 rounds, and 99% of the votes would be sincere. The threat of second
round would be there just to keep the first round "civilised".

And also other candidates than the Smith set candidates. :-)

You could see the second round also only as a technical round where you
consider the candidates to be already known, and you reserve time only for
all the strategic discussions and discussions on what went wrong at the
first round. Also here I'm hoping that the strategic candidates will be
ranked lower at the second round (but realising that also some false claims
of strategic voting might appear :-) ).

In both approaches it makes sense to use a method with good performance
under honesty at the first round.

If there was a strategic three candidate cycle at the first round, maybe
people would reject the candidate whose supporters tried to bury others,
and it would be just a race between the other two top loop candidates, even
if also the second round would use a ranked Condorcet method. Using a
runoff between two candidates would make the second round free of strategic
voting, but might introduce some strategic voting in the first round. A
carefully chosen pair of methods at the first round might eliminate
strategies nicely, but I'm not able to estimate right now, how good the
combination that you presented would be from this point of view.

The philosophy of the two approaches is different. In your proposal the
idea seems to be to use two methods to cancel most strategies out, and in
my proposal to allow people to vote honestly at the first round. There
would be a chance to vote strategically at the second round if the first
round fails to be sincere enough. One could of course go on and use three
rounds, starting from one with ideal performance with sincere votes, and
then proceeding to some more strategy proof method (or combination of
methods), and finally to a two candidate runoff. But of course also
simplicity should have some weight, and this approach might be already too
complex for most needs.

Yes. Have you checked if there are strategic possibilities, trying to push
the election to the second round, trying to vote so that some appropriate
two candidates would go to the second round? The most difficult case might
be one with a sincere three candidate top loop. (Too difficult for me to
get a grip of that right now. :-) )

picking two of them (or some others) for the second round must be hard.
(VSE = Voter Satisfaction Efficiency)

Yes. Strategies are complex, and having two methods trying to fight
together against various combinations of strategies, with different
combinations of defences, makes it even more complex. You could say that I
took the easy way out when proposing an approach where we just hope that
people are sensible enough and do not use strategies, under the protection
of the second round, under the threat of having to vote also at the second
round, having their strategic plans revealed to other voters already at the
first round, and paying a price if voters don't like their strategic games,
and fearing that voters will bullet vote some better and more sincere
candidate, or at least not vote for the strategists, or have some working
counter strategies at the second round. :-)

In some societies people might be more inclined to use strategies and fear
strategies of others more than in some other societies. The approach that I
proposed hopefully makes it one step easier to vote honestly in both cases.
In the best case it would be just a standard Condorcet election with no
need to ever resort to the second round.

BR, Juho

Election-Methods mailing list - see https://electorama.com/em for list info

Hi Kevin!

As I'm sure you remember, I've been trying to figure out a system that
could replace California's "top-two primary" for a while.  Your
proposal could work, but I'm curious about the value it provides over
other approaches.

More inline...

On Fri, Sep 24, 2021 at 5:59 PM Kevin Venzke stepjak@yahoo.fr wrote:

It seems this is the reason for eliminating candidates in the first
round.  If one is going to have approval voting in both rounds, then
requiring a modest approval (e.g. 30% approval) to advance from the
first round to the second round would be ample motivation, even if
several candidates are allowed to advance.  I'm still fond of only
allowing two candidates to advance, so that there's a clear choice
presented to the voters in the second round.

I guess I'm too used to the American primary-election/general-election
split, so I'm wondering what the value is for allowing a candidate to
win with a simple majority in the first round.  It seems like a super
majority (e.g. 60% or higher) should be required to short-circuit a
second-round standoff with the first-round runner up.  Otherwise, it
seems likely to imagine something similar to following scenario with
1,000,000 votes:

A (incumbent) - 500,001 approvals
B (serious challenger) - 499,995 approvals
C (joke challenger) - 10 approvals

That's 6 voters in a 1,000,000 vote election who decide B doesn't get
a head-to-head standoff with A because perhaps some of them got
distracted by C's messaging.  Moreover, since this is approval voting
we're talking about here, it's also possible for this outcome in a
1,000,000 ballot first-round election:

A (incumbent) - 500,100 approvals
B (serious challenger) - 500,050 approvals
C (joke challenger) - 10 approvals

Now, both A and B have slim majorities for their respective approval
ratings.  Perhaps people approved "A" and "B" because "C" seemed like
a real lunatic, and "A" chose to legitimize "C" and ignore "B", and
scaremonger people who would have voted exclusively for "B" into
voting for "A" as well.

It seems to me that it shouldn't be too hard to get candidates and
voters to take the first round seriously.  A small enough
supermajority (e.g. 60%) would seem achievable for a competent
incumbent -- which would cause the rest of the field of candidates to
motivate their base to go to the polls if one candidate getting a
supermajority means  "no second round".

It also seems to me that perhaps the "short-circuit" threshold should
be a large margin (e.g. a 10% lead over the next candidate) rather
than an absolute value (like a 60% supermajority approval).  If two
candidates get over 50% approval in the primary election, it seems
like BOTH candidates should advance to the general election regardless
of the margin, since (by definition) there's a contingent who felt
that both candidates would be acceptable, but (to quote Sean Connery
in Highlander) "there can be only one".  .  If three candidates get
over 50% approval ... well, it sucks to be third place in a primary
where the rules state "only two shall advance".  What seems most
likely in a crowded first round is that no candidates get a majority

Now to reply to your other points:

This seems like an unlikely strategy.  In an approval election, there
seems to be very little strategic reason to not try to get first
place, even if a majority first-place doesn't seem likely.

I think this is the benefit right here.  A tepid response in the
second round would be embarrassing for the FRW, and make it incredibly
difficult to claim a "mandate" on radical policy changes.  It would
also send a message to the opposition that they need to unite in order
to win.  Borrowing an old bit from the Monty Python movie "Life of
Brian", the Judean People's Front and the People's Front of Judea need
to unite against the Romans (so to speak):
https://youtu.be/WboggjN_G-4

Regardess, it's food for thought.  More to think about...

Rob

Hi Rob,

Le samedi 2 octobre 2021, 01:55:40 UTC−5, Rob Lanphier roblan@gmail.com a écrit :

My concern arises from seeing centrist candidates be unable to compete for a major party's
nomination. My hope is that if you present to the voters that a certain candidate is on
track to be elected, it will inspire them to support more choices (assuming they don't like
the projected winner).

So it is not "one on one" but "any and all vs. one."

I don't have an inherent problem with "one on one," and I don't remember what your complaint
was about the California method. I would just be concerned with what is the best way to pick
the finalists.

Hmm? In the American system you can't win with a majority on the first "round" because only
half the political spectrum participates in a contest. Republican and Democratic are done
separately.

If it were possible to win a majority of the electorate during the primaries, you would
practically have to elect that person. Otherwise you have the potential that small changes
in turnout could reverse the result. That would be really bad.

[in my method]

1. It creates incentive to try to win. If there is no reward for winning the first round,
   the first round could return an arbitrary winner when it is supposed to be a strong winner,
   one who is likely to prevail in the second round.

2. I also think getting a majority of the voters to approve you is good enough to get the
   win, especially if our only tool for conducting this race is approval balloting.

3. If a simple majority doesn't win the first round, then I'm not sure what the second round
   is trying to do. My whole goal for the second round was to try to gather a majority when
   there had not been one. If we already had one... Why isn't that the winner?

Ok, but you're talking about a different method if you have a "first-round runner up"
concept.

I don't think you should use "top two" approval to pick finalists, because of the
theoretical possibility that the finalists got their support from the same group of voters.
It may not be very likely to happen, but in theory it's not sound, it doesn't accomplish
anything consistent.

Six voters? I don't follow. You presumably have at most 4 voters who didn't vote for A or B,
not enough to beat A. C can't even be called a spoiler here.

I'm at a loss as to an alternative: Hold a second round, where B might win by the exact same
bare majority that A already had? That seems awfully wasteful, and likely to be viewed as
arbitrary.

To my mind, the purpose of the second round is not to just give B a second shot at it. The
purpose is to see whether some preferences were left unexpressed due to not knowing who was
going to be in the lead. If some candidate can then reach a majority, that's excellent.

Within my method:

1. I can view it as a reward for taking the first round seriously, that the larger majority
   wins.
2. Again my only purpose for the second round was to try to find an elusive majority. Here
   we already have one.

If you're picking finalists, then absolutely, the first round matters.

I'm surprised you feel that way, but maybe it's a common situation in your area.

I don't think the margin has much meaning on approval ballots. I don't totally hate it, but
I wouldn't apply it in cases with a majority.

The possibility here is that candidates find that being FRW is too powerful at uniting opposing
voters against them. Or that being FRW in the second round is an unfair position.

On paper the second round seems a little prejudicial against the FRW. We're checking if any
candidate can defeat the FRW, when the FRW is posited as a likely winner. But any such candidate
will not, in turn, be subjected to this same check. They just win. If such a check were to occur,
or if a different candidate were the FRW, we might find that the original FRW could actually get
a majority. But he has no opportunity to show this.

That's why I'm trying to grant any reasonable perks I can to the FRW, to balance this out.

One hopes.

Kevin